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13 

 

 

 

Article 

Comparative analysis of power consumption 

time series in deprived and developed regions 

of Iran 
Masoud Safarishaal* 

University of Oklahoma Norman, USA 

A R T I C L E   I N F O 
 

Article history: 
Received 22 March 2023  
Received in revised form 
20 April 2023 
Accepted 27 April 2023 
 
Keywords: 
Time series, Load forecasting, Power distribution 
 
*Corresponding author 
Email address:  
masoud.safari@ou.edu  

 
DOI: 10.55670/fpll.fuen.3.1.2 

A B S T R A C T 
 

This paper presents a comparative analysis of power consumption time series 
at 12 o'clock every day between 2020 and 2022 for one distribution network in 
Sistan and one in Tehran. The aim of this study is to compare the development 
and climate differences between these regions, as well as the impact of social, 
industrial, and environmental factors. By comparing a deprived area with an 
area in the capital, we aim to identify potential disparities in power 
consumption and identify potential areas for improvement. We employed the 
CRP tool software and toolkit for time series analysis and used various methods 
to compare and predict the predictability of each time series. Our findings 
suggest significant differences in power consumption between the two regions, 
which could be attributed to socio-economic and environmental factors. 
Overall, this study sheds light on the potential impact of regional differences on 
power consumption and highlights the need for further research in this area. 

 
1. Introduction  

Time series analysis is a statistical technique that 

involves analyzing and modeling patterns in time-varying 

data [1,2]. It is used in many fields, including economics, 

finance, engineering, and the natural sciences [3-4]. One of the 

main goals of time series analysis is to understand the 

underlying processes that generate the data, which can then 

be used to make forecasts and predictions about future values 

[5]. For example, consider a company that wants to forecast 

its monthly sales for the next year. By analyzing historical 

sales data, they can identify trends and seasonal patterns, 

such as increased sales during the holiday season. Using time 

series analysis techniques, they can build models that capture 

these patterns and use them to make accurate predictions 

about future sales. Overall, time series analysis is a powerful 

tool for understanding and predicting patterns in time-

varying data. By using appropriate techniques and models, 

analysts can make accurate forecasts and gain insights into 

the underlying processes that generate the data [6-10]. In this 

study, we compare and analyze two-time series related to 

power consumption at 12 o'clock every day in the period of 

2012 to 2014 for two distribution networks in Sistan and one 

in Tehran. The goal of our analysis is to explore the 

differences in power consumption patterns between these 

two regions and to investigate the impact of various factors 

such as climate, industrial activity, and socio-economic 

conditions on power consumption. To prepare the data for 

analysis, we first normalized the time series to ensure that 

they conform to the assumptions of the time series model. We 

also de-trended the data to remove the effects of long-term 

trends and focus on the underlying patterns in the time series. 

Our analysis reveals interesting differences between the 

power consumption patterns in Sistan and Tehran. For 

example, we observe that the upward trend in power 

consumption is more pronounced in Tehran, possibly due to 

the faster rate of industrial development and population 

growth in the region. We also find that the impact of weather 

conditions on power consumption is more significant in 

Sistan, where most of the power consumption is due to 

household appliances (Figure 1 and Figure 2). Overall, our 

study sheds light on the complex interplay of various factors 

that influence power consumption patterns in different 

regions of Iran. The insights gained from this study can inform 

policy and decision-making related to energy consumption 

and sustainable development in the country. 

2. Histogram Diagram  

A comparison of the histogram diagrams in Figures 3(a) 

and 3(b) reveals that the power consumption in the Sistan 

network is higher than that of the region of Tehran under 

 

 

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February 2024| Volume 03 | Issue 01 | Pages 13-17 

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ISSN 2832-0328 

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M. Safarishaal /Future Energy                                                                                                    February 2024| Volume 03 | Issue 01| Pages 13-17 

14 

 

consideration. However, when the de-trended data in Figure 

3(c) is compared, it becomes apparent that the load 

fluctuations are minimal throughout the year. This aspect is 

highly favorable for the operation of the system, and it makes 

the manufacturing sector more inclined to invest in such 

networks. 

 

Figure 1. Load of Sistan and Tehran 

 

Figure 2. Graph related to the de-trended time series of 

Sistan power consumption and Tehran power consumption 

                                                               

3. False Nearest Neighbor  

Figure 4 displays the False Nearest Neighbor (FNN) plot 

for both time series. This plot is generated using the FNN 

(data) command in MATLAB software and is commonly used 

to estimate the optimal embedding dimension for a time 

series. The FNN plot reveals that the Sistan time series has a 

dimension of 8, while the Tehran time series has a dimension 

of 7. This suggests that the Sistan time series exhibits less 

predictability and is more challenging to forecast accurately. 

4. Mutual Information (MI) 

Figure 5 displays the result of applying the mi (data) 

command, which utilizes the mutual information method to 

estimate the delay in the time series. The delay is found to be 

6 for Sistan and 5 for Tehran, as determined by identifying the 

first minimum of the chart. Additionally, the False Nearest 

Neighbor (FNN) graph in Figure 4 shows that the Sistan time 

series has a dimension of 8 while the Tehran time series has a 

dimension of 7. These findings indicate that the Sistan 

network is less predictable and more difficult to forecast than 

the Tehran network. The fuzzy body diagram demonstrates 

that the behavior of both time series is chaotic, which 

suggests that they have limited predictability. 

 

 

 

 

 

 

 

 

 

 

 

 

 

(a) 

(b) 

(c) 

Figure 3. hist diagram: (a) Tehran (b) Sistan (c) detrend 

Tehran and Sistan 

 

5. Cross Recurrent Plot 

Figure 6 illustrates the cross-recurrence plot for both 

power consumption time series, revealing the chaotic nature 

of both systems. However, the plot for the Tehran network 

shows a higher number of parallel lines. As confirmed by 

previous methods, this indicates that the Tehran time series 

is more predictable than the Sistan time series. Notably, the 

large squares in the plot for the Sistan time series reveal its 

seasonal behavior, which was previously observed in the time 

series diagram. 

6. xcf diagram 

 Figure 7 displays the cross-correlation function (xcf) 

diagram for both time series. The xcf command is used to 

measure the correlation between the data sets. The diagram 

shows that the correlation between the data in Tehran is very 

high, indicating that the data is closely related to each other. 

This high level of correlation makes it easier to predict the 

behavior of the data. 

 

 



M. Safarishaal /Future Energy                                                                                                    February 2024| Volume 03 | Issue 01| Pages 13-17 

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Figure 4. False Nearest Neighbor (FNN) 

 

(a) 

 

(b) 

 

Figure 5. MI. (A) Tehran (b) Sistan 

 

7. Power Spectrum Density 

The power spectrum density diagrams in Figure 8 were 

generated using the psd (data) command. These diagrams 

show the distribution of power across different frequencies in 

the time series data. Specifically, the density spectral integral 

plots the average signal strength over a range of frequencies. 

This analysis can provide insights into the dominant 

frequencies present in the time series and can be useful in 

identifying periodic patterns or trends. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(a) 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(b) 

 

Figure 6. Diagram of cross recurrent plot (a) Tehran (b) 

Sistan 

 

Figure 9 shows the phase space diagram for both time 

series in a 3D display. A phase space diagram is a useful tool 

for visualizing the behavior of a dynamical system in three 

dimensions. It plots the system's state variables against each 

other, with each axis representing a different variable. The 

resulting pattern of points can reveal the underlying structure 

of the system, such as periodicity, chaos, or other types of 

dynamics. 

In this case, the phase space diagram shows that both 

time series exhibit chaotic behavior, as evidenced by the 

irregular and unpredictable pattern of points in the 3D space. 

This confirms the findings from the other methods used in 

this study, which also indicated that the time series are 

difficult to predict due to their chaotic nature. 

Overall, the phase space diagram provides additional 

insight into the underlying dynamics of the power 

consumption time series and reinforces the need for 

sophisticated forecasting methods that can account for the 

complex and unpredictable behavior of these systems. 

 

 

 

 

 



M. Safarishaal /Future Energy                                                                                                    February 2024| Volume 03 | Issue 01| Pages 13-17 

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(a) 

Figure 7. xcf diagram: (a) Tehran (b) Sistan 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

                                            

 

 

 

 

(a) 

 

 

 

 

 

 

 

(b) 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(b) 

 

 

 

 

 

 

 

Figure 8. psd diagram of two time series 

    Figure 9. Phase body diagram for a) Sistan and b) Tehran time series 

 



M. Safarishaal /Future Energy                                                                                                    February 2024| Volume 03 | Issue 01| Pages 13-17 

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8. Conclusion  

In this study, we analyzed and compared two-time series 

related to power consumption at 12 o'clock every day in 2020 

and 2022 for two distribution networks in Sistan and one in 

Tehran. Our analysis revealed that the seasonal power 

consumption in Sistan is significantly impacted by weather 

conditions, as most power consumption in Sistan is due to 

household appliances. In contrast, power consumption in 

Tehran is less dependent on weather conditions and is driven 

more by the city's industrial nature, which makes it more 

predictable. We also found that the upward trend in power 

consumption in Tehran is primarily due to the city's faster 

development and population growth, whereas Sistan, being a 

deprived area, has not experienced many changes in power 

consumption during the two years. Finally, we observed that 

the difference in power consumption between seasons is 

more pronounced in Sistan compared to Tehran. Overall, our 

findings suggest that regional disparities in power 

consumption are closely linked to socio-economic and 

environmental factors, and further research in this area is 

needed to inform future policies and initiatives aimed at 

promoting sustainable development in different regions of 

Iran. 

Ethical issue 

The author is aware of and complies with best practices in 
publication ethics, specifically concerning authorship 
(avoidance of guest authorship), dual submission, 
manipulation of figures, competing interests, and compliance 
with policies on research ethics. The author adheres to 
publication requirements that the submitted work is original 
and has not been published elsewhere in any language. 

Data availability statement 
Datasets analyzed during the current study are available and 

can be given following a reasonable request from the 

corresponding author. 

Conflict of interest 

The author declares no potential conflict of interest. 

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 This article is an open-access article 

distributed under the terms and conditions of the Creative 

Commons Attribution (CC BY) license 

(https://creativecommons.org/licenses/by/4.0/). 


